Cremona's table of elliptic curves

10580 = 2² · 5 · 23²

Field	Data	Notes
Atkin-Lehner	2- 5+ 23-	Signs for the Atkin-Lehner involutions
Class	10580a	Isogeny class
Conductor	10580	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	18144	Modular degree for the optimal curve
Δ	5596820000000 = 28 · 57 · 234	Discriminant
Eigenvalues	2-  0 5+  2  3 -6 -2  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-16928,840052]	[a1,a2,a3,a4,a6]
Generators	[69:23:1]	Generators of the group modulo torsion
j	7488405504/78125	j-invariant
L	4.2163441726163	L(r)(E,1)/r!
Ω	0.76406528676781	Real period
R	1.8394345115247	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	42320j1 95220z1 52900f1 10580h1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 10580a1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	0	+	2	3	-6	-2	5	-	-2	1	4	5	-4	2	12	-8	1	-6	1	-2	-9	4	-6	8

---

Quadratic twists for elliptic curve 10580a1

-4	-3	5	-23
42320j1	95220z1	52900f1	10580h1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations